Evaporative cooling devices such as heat pipes and capillary pumped loops utilize capillary suction to draw liquid into the evaporation region. This capillary suction results from the pressure differential across the phase interface between a liquid and vapor. According to the Laplace-Young relation, the interfacial pressure difference is proportional to the surface tension and is inversely proportional to the radius of curvature of the interface. Further, since the pressure within the liquid is generally less than that in the adjacent gas, the liquid pressure decreases as the radius of curvature becomes smaller. Thus, liquid is drawn toward regions where the radius of curvature is small and the liquid pressure is low.
In the typical heat pipe configuration of FIG. 1 heat is applied at one end causing evaporation of liquid from the wick. The vapor generated raises the gas phase pressure at the hot end causing transport of vapor along the open center toward the cold end. Heat extraction at the cold end condenses the vapor. The condensate is absorbed by the wick and then transported through the wick by capillary suction back to the hot region where the liquid pressure is lower.
The capillary pumped loop of FIG. 2 is similar in concept except that the evaporator and the condenser units are connected by a pair of tubes or channels that facilitate greater separation between the heat source and sink, particularly in cases where space is limited. In this device the capillary suction of the wick must overcome the viscous friction in the connector tubes as well as the friction within the wick itself. However, it is also true that the capillary suction of a heat pipe must overcome the frictional pressure drops in both phases, and in that configuration the counterflow of the vapor and liquid adds to the overall flow resistance.
In traditional evaporative cooling devices the wick is constructed of a porous material such as a sintered metal, a felt metal, or a layered screen (see A. Faghri “Heat Pipe Science and Technology” Taylor and Francis Publishers, 1995). Metals are used because high thermal conductivity is needed to transfer heat through the wick to the liquid/vapor interface where evaporation is intended to occur, thus avoiding bubble formation within the wick. The performance of a wick material is strongly dependent upon its microstructure. It is generally beneficial to have relatively small pores or interstices within the material since this reduces the minimum radius of curvature of the phase interface, increasing the capillary pressure difference available to draw liquid into the wick. However, smaller pores result in greater frictional resistance and, hence, slower rates of liquid transport through the wick. Thus, the optimum pore size must strike a balance between these opposing requirements.
Engineered wick structures are now being produced by modem microfabrication techniques. Electrical discharge machining (EDM) of metals and chemical etching of silicon have been used to create microgrooves having triangular, trapezoidal, sinusoidal, and nearly rectangular cross sections (Stores, et al., Proceedings of the 28th National Heat Transfer, Aug. 9-12, San Diego, v. 200, 1992, pp. 1-7; and Journal of Heat Transfer, v. 119, 1997, pp. 851-853 and Sivaraman, et al., International. Journal of Heat and Mass Transfer, v.45,2002, pp.1535-1543). Of these alternative shapes, triangular grooves have received by far the most attention (Xu, et al., Journal of Thermophysics, v. 4, no.4, 1990, pp. 512-520; Ha, et al., Journal of Heat Transfer, v. 118, 1996, pp. 747-755; Peles, et al., International Journal of Multiphase Flow, v. 26, 2000, pp. 1095-1115; and Catton, et al., Journal of Heat Transfer, v. 124, 2002, pp. 162-168). The focus on this geometry may be largely because it provides a monotonic decrease in meniscus radius and capillary pressure as the depth of the fluid decreases and the meniscus recedes into the wedge-shaped channel, as illustrated in FIG. 3A. However, the triangular shape provides only half the cross-sectional area of a rectangular channel, the viscous friction is greater and, in addition, deep triangular cross sections cannot be readily produced using lithographic processes that have been so successful in mass production of semiconductor devices.
Lithographic processes are well suited to the fabrication of devices having a great multiplicity of highly detailed microscale features. In particular, the LIGA process can be used to produce a multiplicity of metal channels having widths down to a few microns and depths as large as a millimeter or more (see Becker, et al., Microelectronic Engineering, v. 4, 1986, pp. 35-56; and Ehrfeld, et al., Journal of Vacuum Science and Technology (B), v. 16, no.6, 1998, pp. 3526-3534). In LIGA, a high-energy x-ray source is used to expose a thick photoresist, typically PMMA, through a patterned absorber mask. The exposed material is then removed by chemical dissolution in a development bath. This development process yields a nonconducting mold having a conducting substrate beneath deep cavities that are subsequently filled by electrodeposition. The resulting metal parts may be the final product or may be used as injection or embossing molds for mass production. However, since the exposure beam is generally aligned perpendicular to the patterned mask, LIGA and other lithographic processes are best suited for fabrication of channels having parallel sidewalls and hence a rectangular cross section. Multiple x-ray exposures at different angles to the mask could be used to produce triangular channels, but not without added complexity and loss of precision.
Although amenable to LIGA fabrication, straight rectangular microchannels have one notable disadvantage. As illustrated in FIG. 3B, the capillary pressure varies with the liquid height (depth) in the channel only so long as the meniscus remains attached to the top comers of the channel. The radius of curvature of the interface may then range anywhere between infinity for a flat meniscus to a minimum radius that corresponds to the minimum wetting angle. However, once the meniscus recedes into the channel and leaves the singular corner point, the wetting angle is fixed at a particular minimum value determined by liquid and solid interaction energies. Thus there is a large range of liquid heights (depths) in the channel for which the radius of curvature and the corresponding capillary pressure are invariant. Within this “dead zone” (see Stores, et al.; Journal of Heat Transfer, v. 119, 1997, pp. 851-853) there will be no capillary pressure variation to draw fluid toward the drier end of the channel. It is only when the meniscus reaches the channel bottom and begins to recede into the corners that a capillary pressure gradient can again be established. But in this regime the fluid depth can be no greater than half the channel width.